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  1. A Metropolis Algorithm (named after Nicholas Metropolis, a poker buddy of Dr. Ulam) is a commonly used MCMC process.[1]
  2. Of course, this is a highly simplified example, and MCMC algorithms can be created for continuous and multi-parameter distributions.[1]
  3. If the target distribution has a sparser density in that region, the estimates produced from the MCMC will be biased.[1]
  4. There are many other sampling algorithms for MCMC.[1]
  5. Strict detailed balance is not necessary for Markov chain Monte Carlo simulations to converge to the correct equilibrium distribution.[2]
  6. Indeed, MCMC is indispensable for performing Bayesian analysis.[3]
  7. Two critical questions that MCMC practitioners need to address are where to start and when to stop the simulation.[3]
  8. This review article discusses the most widely used MCMC convergence diagnostic tools.[3]
  9. A common way to obtain approximate samples from such distributions is to make use of Markov chain Monte Carlo (MCMC) algorithms.[4]
  10. Two questions arise when using MCMC algorithms.[4]
  11. This chapter provides insight into how to answer both of these questions in the course of describing how MCMC algorithms are used in practice.[4]
  12. In this chapter, common types of MCMC algorithms are described, and Bayesian estimation using the output of the chain is also discussed.[4]
  13. The Markov chain Monte Carlo (MCMC) method, as a computer‐intensive statistical tool, has enjoyed an enormous upsurge in interest over the last few years.[5]
  14. We begin by discussing how MCMC algorithms can be constructed from standard building‐blocks to produce Markov chains with the desired stationary distribution.[5]
  15. We discuss some implementational issues associated with MCMC methods.[5]
  16. We also take a look at graphical models and how graphical approaches can be used to simplify MCMC implementation.[5]
  17. MCMC approaches represent a formal Bayesian inference, since the likelihood function is statistically rigorous given the error model e(φ).[6]
  18. Pseudo-code for the MCMC methods used in this study.[7]
  19. a Multiple MCMC runs per scenario.[7]
  20. In this manuscript, we determine the EQ by first grouping individual MCMC runs of the same benchmark problem and then identify groups with members which explored the relevant parameter space well.[7]
  21. Here we present a Markov chain Monte Carlo method for generating observations from a posterior distribution without the use of likelihoods.[8]
  22. The practical complexities of implementing MCMC are described by Gilks et al.[8]
  23. One therefore expects that MCMC approaches accept observations more frequently, but the price paid for higher acceptance rates is dependent outcomes.[8]
  24. In this section we describe an MCMC approach that is the natural analog of algorithm B in that no likelihoods are used or estimated in its implementation.[8]
  25. An adaptive Markov chain Monte Carlo simulation approach is proposed to evaluate the desired integral that is based on the Metropolis-Hastings algorithm and a concept similar to simulated annealing.[9]
  26. The intuition gained by studying these orderings is used to improve existing Markov chain Monte Carlo algorithms.[10]
  27. Randomized reduced forward models for efficient Metropolis–Hastings MCMC, with application to subsurface fluid flow and capacitance tomography.[11]
  28. Markov Chain Monte Carlo Methods for Fluid Flow Forecasting in the Subsurface.[11]
  29. A transport-based multifidelity preconditioner for Markov chain Monte Carlo.[11]
  30. A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media.[11]
  31. This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step.[12]
  32. Markov Chain Monte Carlo sampling provides a class of algorithms for systematic random sampling from high-dimensional probability distributions.[13]
  33. MCMC is essentially Monte Carlo integration using Markov chains.[13]
  34. MCMC methods allow us to estimate the shape of a posterior distribution in case we can’t compute it directly.[14]
  35. Recall that MCMC stands for Markov chain Monte Carlo methods.[14]
  36. In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution.[15]
  37. Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function.[15]
  38. However, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC are autocorrelated.[15]
  39. In principle, any Markov chain Monte Carlo sampler can be turned into an interacting Markov chain Monte Carlo sampler.[15]
  40. One can use MCMC to draw samples from the target distribution, in this case the posterior, which represents the probability of each possible value of the population mean given this single observation.[16]
  41. To draw samples from the distribution of test scores, MCMC starts with an initial guess: just one value that might be plausibly drawn from the distribution.[16]
  42. MCMC is then used to produce a chain of new samples from this initial guess.[16]
  43. If the new proposal is accepted, it becomes the next sample in the MCMC chain, otherwise the next sample in the MCMC chain is just a copy of the most recent sample.[16]
  44. Markov chain Monte Carlo is one of our best tools in the desperate struggle against high-dimensional probabilistic computation, but its fragility makes it dangerous to wield without adequate training.[17]
  45. Unfortunately the Markov chain Monte Carlo literature provides limited guidance for practical risk management.[17]
  46. Before introducing Markov chain Monte Carlo we will begin with a short review of the Monte Carlo method.[17]
  47. Finally we will discuss how these theoretical concepts manifest in practice and carefully study the behavior of an explicit implementation of Markov chain Monte Carlo.[17]
  48. In §2, the fundamental principles behind a Bayesian approach to system identification are described and the benefits of using MCMC algorithms within a Bayesian framework are emphasized.[18]
  49. Sections 3 and 4 are devoted to the description of various MCMC algorithms which can be used to address the issues of parameter estimation and model selection, respectively.[18]
  50. than(one may try to achieve this using the Metropolis algorithm or other MCMC methods).[18]
  51. Ultimately, with each sample generated using MCMC requiring a model run, the applicability of MCMC to Bayesian system identification problems is limited by computational cost.[18]
  52. Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality.[19]
  53. Hence, Markov Chain Monte Carlo (MCMC) approaches have been frequently used to estimate posterior distributions of rate parameters.[20]
  54. However, designing a good MCMC sampler for high dimensional and multi-modal parameter distributions remains a challenging task.[20]
  55. Here we performed a systematic comparison of different MCMC techniques for this purpose using five public domain models.[20]
  56. The comparison included Metropolis-Hastings, parallel tempering MCMC, adaptive MCMC, and parallel adaptive MCMC.[20]
  57. Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods.[21]
  58. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation.[22]
  59. Markov chain Monte Carlo (MCMC) is a method for exploring the calibration of a model.[23]
  60. Simplistically, MCMC performs a random walk on the likelihood surface specified by the payoff function.[23]
  61. The MCMC algorithm is closely related to Simulated Annealing (SA), in that both explore a surface stochastically, using the Metropolis acceptance criterion for proposed points.[23]
  62. The MCMC routine may be accessed in two ways: as a payoff sensitivity method, following a Powell optimization, and as a standalone estimation (MCMC) or optimization (SA) method.[23]
  63. Popular MCMC samplers and their alignment with Bayesian approaches to modeling are discussed.[24]
  64. The last decade has seen an explosion in the use of Markov chain Monte Carlo (MCMC) techniques in fitting statistical psychometric models.[24]
  65. In this time, MCMC has been put to advantageous use in estimating existing models and, more importantly, supporting the development of new models that are otherwise computationally intractable.[24]
  66. As will be highlighted below, key features of the most flexible of MCMC algorithms may be viewed as explicitly resolving the most difficult challenges in estimating Bayesian models.[24]

소스

  1. 1.0 1.1 1.2 1.3 Markov Chain Monte Carlo
  2. Acceleration of Markov chain Monte Carlo simulations through sequential updating
  3. 3.0 3.1 3.2 Convergence Diagnostics for Markov Chain Monte Carlo
  4. 4.0 4.1 4.2 4.3 Markov chain Monte Carlo methods: Theory and practice
  5. 5.0 5.1 5.2 5.3 Markov chain Monte Carlo method and its application
  6. Markov Chain Monte Carlo - an overview
  7. 7.0 7.1 7.2 Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems
  8. 8.0 8.1 8.2 8.3 Markov chain Monte Carlo without likelihoods
  9. Bayesian Updating of Structural Models and Reliability using Markov Chain Monte Carlo Simulation
  10. Mira : Ordering and Improving the Performance of Monte Carlo Markov Chains
  11. 11.0 11.1 11.2 11.3 Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
  12. Markov Chain Monte Carlo Simulations and Their Statistical Analysis
  13. 13.0 13.1 A Gentle Introduction to Markov Chain Monte Carlo for Probability
  14. 14.0 14.1 A Zero-Math Introduction to Markov Chain Monte Carlo Methods
  15. 15.0 15.1 15.2 15.3 Markov chain Monte Carlo
  16. 16.0 16.1 16.2 16.3 A simple introduction to Markov Chain Monte–Carlo sampling
  17. 17.0 17.1 17.2 17.3 Markov Chain Monte Carlo in Practice
  18. 18.0 18.1 18.2 18.3 Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty
  19. Geyer : Practical Markov Chain Monte Carlo
  20. 20.0 20.1 20.2 20.3 MCMC Techniques for Parameter Estimation of ODE Based Models in Systems Biology
  21. Markov Chain Monte Carlo
  22. Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
  23. 23.0 23.1 23.2 23.3 Reference Manual > Advanced Simulation Methods > Optimization > Markov Chain Monte Carlo & Simulated Annealing
  24. 24.0 24.1 24.2 24.3 The Rise of Markov Chain Monte Carlo Estimation for Psychometric Modeling

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